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Resolución de integrales/ ln(2x)/ x*sqrt/ 1/(x*sqrt(ln(2x)^2-3))

Integral de 1/(x*sqrt(ln(2x)^2-3)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                        
  /                        
 |                         
 |           1             
 |  -------------------- dx
 |       _______________   
 |      /    2             
 |  x*\/  log (2*x) - 3    
 |                         
/                          
0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{\log{\left(2 x \right)}^{2} - 3}}\, dx$$ 
Integral(1/(x*sqrt(log(2*x)^2 - 3)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                /                                                  
 |                                |                                                   
 |          1                     |                        1                          
 | -------------------- dx = C +  | ----------------------------------------------- dx
 |      _______________           |      __________________________________________   
 |     /    2                     |     /         2         2                         
 | x*\/  log (2*x) - 3            | x*\/  -3 + log (2) + log (x) + 2*log(2)*log(x)    
 |                                |                                                   
/                                /
$$\int \frac{1}{x \sqrt{\log{\left(2 x \right)}^{2} - 3}}\, dx = C + \int \frac{1}{x \sqrt{\log{\left(x \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(x \right)} - 3 + \log{\left(2 \right)}^{2}}}\, dx$$
Simplificar
Respuesta [src] 
  1                                                   
  /                                                   
 |                                                    
 |                         1                          
 |  ----------------------------------------------- dx
 |       __________________________________________   
 |      /         2         2                         
 |  x*\/  -3 + log (2) + log (x) + 2*log(2)*log(x)    
 |                                                    
/                                                     
0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{\log{\left(x \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(x \right)} - 3 + \log{\left(2 \right)}^{2}}}\, dx$$ 
=
= 
  1                                                   
  /                                                   
 |                                                    
 |                         1                          
 |  ----------------------------------------------- dx
 |       __________________________________________   
 |      /         2         2                         
 |  x*\/  -3 + log (2) + log (x) + 2*log(2)*log(x)    
 |                                                    
/                                                     
0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{\log{\left(x \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(x \right)} - 3 + \log{\left(2 \right)}^{2}}}\, dx$$ 
Integral(1/(x*sqrt(-3 + log(2)^2 + log(x)^2 + 2*log(2)*log(x))), (x, 0, 1))
Respuesta numérica [src] 
(4.54044985849606 - 1.80140546830524j)
(4.54044985849606 - 1.80140546830524j)

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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